[cmath] Re: [Cmesg-l] Fwd: Good article for promoting pure math research

[Walter Whiteley]

Miroslav

	I think it is valuable to separate several factors here to generate a  
more nuanced conclusion:

- unplanned impact:  this arises often within applied math as well and  
many other areas.
  	Unplanned impact is indeed a feature of human creativity in almost  
every field.  This is an important point for funders and people making  
decisions in every field (not specific to 'pure mathematics').  It is  
also important for students in general - but part of the message is to  
look for, even seek out, unplanned connections and impact.

- explorations of a  'pure mathematical nature' as done by many  
stripes of mathematicians, in many settings, which is distinct from   
the fields of "pure mathematics" as something done full time  
(sometimes with pride at having no applications).

	For example consider the discussion of topology in the article.   
Topology is something young children explore (before they explore  
straight lines, area, volume .... ) - what spaces can I 'reach' -  
which door can I exit and then come back though another door ... .    
Parts of topology are something Mobius explored (what we now call  
oriented cell complexes) - while doing developing barycentric  
coordinates to give a good exposition of statics, working out oriented  
and non-oriented surfaces (signed volumes etc.), as well as doing  
astronomy and other work.  Topology is something Poincare did - while  
coming very close to publishing relativity theory at the same time as  
Einstein.
	That subject of topology is not, never really was, purely abstract/ 
theoretical non-applicable.
Of course, people may wander into topics while not currently motivated  
by applications (but still grounded, like all human thinking, in  
experiences, in imaginative possibilities connecting/blending concepts  
and samples, experienced over time.

	I learned topology (homology) as 'pure mathematics' - and then  
relearned it in several applied contexts.   My instructor actually  
knew some of these areas of application - but chose not to offer that  
added context which would have helped my learning (including the  
techniques I memorized for a comprehensive exam then forgot!).

  	When talking with my students, I discuss the history of math.  My  
understanding is that up to post 1900, everyone we talk about was  
doing what is now called both pure and applied mathematics, and often  
several other subjects as well.   To me, for anyone to do 'only pure  
mathematics' is a temporary aberration within the larger flow of  
mathematics with all its connections to human processes, as well as  
connections to other puzzles across a range of activities we try to  
solve with mathematics.

Walter Whiteley

On 14-Jul-11, at 10:51 PM, Miroslav Lovric wrote:

>
>
> Peter,
>
> thank you very much for this
>
> Some of the stories/case studies I know about, and always talk about  
> them
> to my students. Now I know more stories!
>
> Important message -- for students, as well as for teachers, math
> curriculum people, etc. -- is that not every piece of math
> needs to be (or can be) justified by some (present-day, "real life")
> application.
>
> There is huge value in learning about (and researching) areas of  
> math that
> seem to be "purely abstract/theoretical" or "non applicable."
>
> Cheers
> Miroslav
>
>
>
>
>
>
>
> On Thu, 14 Jul 2011 11:34:19 -0400
> Peter Taylor <peter.taylor at queensu.ca> wrote:
>> Steve La Rocque brought to my attention a commentary article in  
>> Nature which
>> came out today celebrating the unanticipated impact of mathematics  
>> research.
>> It's great to see such articles in Nature and it's certainly timely  
>> for us
>> in Canada(!)  At the bottom of the article there is a useful link  
>> to the work
>> of the British Society for the History of Math in collecting  
>> interesting
>> stories about applications.
>> peter
>>
>> The unplanned impact of mathematics
>> Nature 475, 166–169 (14 July 2011)
>> <http://dx.doi.org/10.1038/475166a>doi:10.1038/475166a
>> Published online 13 July 2011
>>
>> Nature url:
>>
> <http://www.nature.com/nature/journal/v475/n7355/full/475166a.html>http://www.nature.com/nature/journal/v475/n7355/full/475166a.html
>> Shortform url: <http://bit.ly/nbsY5B>http://bit.ly/nbsY5B
>>
>>
>>
>> Peter Taylor
>> Professor
>> Dept Math&Stats
>> Queen's University
>> Kingston ON K7L 3N6
>> 613 533-2434
>> http://www.mast.queensu.ca/~peter/
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>
> * * * * * * ************************************************
>  Miroslav Lovric
>  Professor
>  Department of Mathematics and Statistics
>  McMaster University
>  Hamilton, Ontario L8S 4K1, Canada
>
>  tel.: 905.525.9140.ext27362
>  fax:  905.522.0935 (attn. M.Lovric)
>  e-mail: lovric at mcmaster.ca
>  http://www.math.mcmaster.ca/lovric/lovric.html
> ************************************************************
>
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